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Asymptotic Expansions for q-Gamma, q-Exponential, and q-Bessel Functions

✍ Scribed by A.B.O. Daalhuis

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
505 KB
Volume
186
Category
Article
ISSN
0022-247X

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πŸ“œ SIMILAR VOLUMES

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q-Analogues are given for the limit formulas e'=lim,+,(l -t/n)-' and e'=lim,,, (1 + t/n)'. The q-extension of the first identity is applied in proving that the probability of a q-random mapping having no fixed points approaches the reciprocal of a q-analogue of the real number e.

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An addition and product formula for the Hahn Exton \(q\)-Bessel function, previously obtained by use of a quantum group theoretic interpretation, are proved analytically. A (formal) limit transition to the Graf addition formula and corresponding product formula for the Bessel function is given. 1995

Sharp Bounds for the Ratio of q – Gamma
Sharp Bounds for the Ratio of q – Gamma Functions
✍ Horst Alzer πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 148 KB πŸ‘ 2 views

Let Ξ“q (0 < q = 1) be the q -gamma function and let s ∈ (0, 1) be a real number. We determine the largest number Ξ± = Ξ±(q, s) and the smallest number Ξ² = Ξ²(q, s) such that the inequalities hold for all positive real numbers x. Our result refines and extends recently published inequalities by Ismail